Generation of hydromagnetic and ion cyclotron waves by an induction coil is considered for a cylindrical plasma in a uniform confining magnetic field. Resonance widths are calculated and power absorption is calculated and compared to ohmic losses in the induction coil. Rapid thermalization of transverse plasma waves occurs when appreciable numbers of ions stream through the periodic perturbation with velocities such that, in their own rest frames, these ions ``feel'' the perturbation at their own cyclotron frequency. This effect, termed cyclotron damping, makes possible an efficient plasma heating scheme for thermonuclear reactors. Radio‐frequency power can be transferred from an induction coil into ion cyclotron waves with an efficiency typically greater than 65&percent;. The wave energy can be quickly transformed into energy of effectively random transverse ion motion by causing the ion cyclotron wave to travel along a magnetic field which decreases slowly with distance.